## The Annals of Probability

### Strong Limit Theorems for Large and Small Increments of $l^p$-Valued Gaussian Processes

#### Abstract

Based on the well-known Borell inequality and on a general theorem for large and small increments of Banach space valued stochastic processes of Csaki, Csorgo and Shao, we establish some almost sure path behaviour of increments in general, and moduli of continuity in particular, for $l^p$-valued, $1 \leq p < \infty$, Gaussian processes with stationary increments. Applications to $l^p$-valued fractional Wiener and Ornstein-Uhlenbeck processes are also discussed. Our results refine and extend those of Csaki, Csorgo and Shao.

#### Article information

Source
Ann. Probab., Volume 21, Number 4 (1993), 1958-1990.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176989007

Digital Object Identifier
doi:10.1214/aop/1176989007

Mathematical Reviews number (MathSciNet)
MR1245297

Zentralblatt MATH identifier
0791.60028

JSTOR
Csorgo, Miklos; Shao, Qi-Man. Strong Limit Theorems for Large and Small Increments of $l^p$-Valued Gaussian Processes. Ann. Probab. 21 (1993), no. 4, 1958--1990. doi:10.1214/aop/1176989007. https://projecteuclid.org/euclid.aop/1176989007